This book offers a detailed introduction into the field of quantum mechanics applied to nuclear structure, and is intended for as a primer for nuclear physics graduate students and postgraduate students seeking a solid foundation in the subject.
Author(s): Kris Heyde, John Wood
Series: IOP Series in Nuclear Spectroscopy and Nuclear Structure
Publisher: IOP Publishing
Year: 2020
Language: English
Pages: 229
City: Bristol
PRELIMS.pdf
Preface
Author biographies
Kris Heyde
John L Wood
CH001.pdf
Chapter 1 A theory of polarized photons
1.1 Polarized lightwaves
1.2 Polarized photons
1.3 Uncertainty in experiments
1.4 Dirac bracket notation
1.5 Transformation properties of polarizing filter measurements
1.6 Multiples of kets
1.7 Exercises
Reference
CH002.pdf
Chapter 2 A theory of the Stern–Gerlach experiment for spin-12 particles
2.1 The Stern–Gerlach experiment
2.2 Sequences of Stern–Gerlach measurements
2.3 State representation for spin-12 particles
2.3.1 Representation with respect to mutually orthogonal axes
Example 2.1
Example 2.2
Example 2.3
2.3.2 Representation with respect to arbitrary axes
2.4 The choice of basis kets
2.5 Exercises
2.6 An introduction to operators for spin-12 particles
2.6.1 Outer products of kets and bras as operators
2.6.2 Column vectors, row vectors, and matrices
2.6.3 Non-commutation of operators
2.6.4 The cone of uncertainty for quantum spin-12 particles
2.7 Exercises
Reference
CH003.pdf
Chapter 3 The axioms of quantum mechanics
3.1 Global axioms of observation
3.2 Axioms for quantum mechanical observations
3.3 Axioms for the mathematical structure of quantum mechanics
3.4 Axioms for the incorporation of ℏ in quantum mechanics
3.5 Exercise
CH004.pdf
Chapter 4 Linear spaces and linear operators
4.1 Definitions and theorems for linear spaces and linear operators
4.2 Linear spaces, Dirac bras and kets, and operators
4.3 Outer products of Dirac bras and kets
4.4 Exercises
CH005.pdf
Chapter 5 The harmonic oscillator
5.1 The quantum mechanical one-dimensional harmonic oscillator
5.2 The quantum mechanical two-dimensional harmonic oscillator
5.3 Time dependence of the one-dimensional quantum harmonic oscillator
5.4 Exercises
5.5 Coherent states and the one-dimensional harmonic oscillator
CH006.pdf
Chapter 6 Representations: matrices
6.1 Basics of matrix manipulation
6.2 Exercises
6.3 The two-level mixing problem
6.4 Exercises
6.5 Unitary transformations and matrix diagonalization
6.6 Exercises
6.7 Matrix diagonalization: the Jacobi method
6.7.1 Example
6.8 Exercise
References
CH007.pdf
Chapter 7 Observables and measurements
7.1 Basic concepts
7.2 The uncertainty relation
7.3 Exercises
7.4 Mixtures and the density matrix
CH008.pdf
Chapter 8 Representations: position, momentum, wave functions, and function spaces
8.1 The concept of a wave function
8.2 The quantum mechanical structure of position and momentum
8.3 The wave-like properties of matter
8.4 Exercises
References
CH009.pdf
Chapter 9 Quantum dynamics: time evolution and the Schrödinger and Heisenberg pictures
9.1 Basic relations
9.2 Spin precession
9.3 Exercises
9.4 Correlation amplitude and the energy–time uncertainty relation
9.5 The Schrödinger and Heisenberg pictures
9.6 The free particle in the Heisenberg picture
9.7 Schrödinger’s wave equation
9.8 Exercises
9.9 Alternative derivation of the energy–time uncertainty relation
9.10 Time-dependent phenomena
9.11 Time-dependent two-state problems
9.12 Exercise
Reference
CH010.pdf
Chapter 10 Rotations and continuous transformation groups
10.1 Elements of group theory
10.2 Matrix groups
10.3 Exercises
10.4 Rotations in physical space
10.5 Exercise
10.6 Rotations of quantum mechanical states
10.7 Exercise
CH011.pdf
Chapter 11 Angular momentum and spin in quantum mechanics
11.1 The algebra of angular momentum in quantum mechanics
11.2 Algebraic solution of the quantum mechanical angular momentum problem
11.3 Exercises
CH012.pdf
Chapter 12 Central force problems
12.1 General features of central force problems
12.2 Central force problems, factorization algebra and isospectral Hamiltonians
12.3 The hydrogen atom central force problem
12.4 The three-dimensional isotropic harmonic oscillator central force problem
12.5 The three-dimensional isotropic infinite square well central force problem
12.6 Exercises
12.7 Central force problems and so(2, 1) or su(1, 1) algebra
12.8 so(2, 1) solution for the hydrogen atom
Comments
12.9 so(2, 1) solution for the three-dimensional isotropic harmonic oscillator
References
CH013.pdf
Chapter 13 Motion of an electron in a uniform magnetic field
13.1 Maxwell’s equations
13.2 The Landau level problem
13.3 Time dependence of the Landau problem
13.4 Exercises
Reference
APP1.pdf
Chapter
A.1 Basic definitions
A.2 Secondary relations
APP2.pdf
Chapter
B.1 Hydrogen atom
B.2 Three-dimensional isotropic harmonic oscillator
